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2.1 Derivatives and Rates of Change

# 2.1 Derivatives and Rates of Change - The derivative is...

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Derivatives and Rates of Change Section 2.1

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Average Rate of Change l The average rate of change of a quantity over a period of time is the amount of change divided by the time it takes. l The average rate of change over the interval [a, b] = ( ) ( ) f b f a b a - -
Slope of Secant Line (c, f(c)) (c + ,f(c + ) x x ) ( ) ( c f x c f - + x x x c f x c f m - + = ) ( ) ( sec

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Average Rate of Change
Slope of a Tangent Line: derivative of f at a number a l The slope of the curve y=f(x) at the point P(a, f(a)) is the number provided the limit exists.

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Unformatted text preview: The derivative is also considered the instantaneous rate of change. ( ) ( ) '( ) lim → +-= = h f a h f a f a m h Slope of a Tangent Line (derivative) at a point P (a, f(a)) Normal to a Curve l The normal line to a curve at a point is the line perpendicular to the tangent at that point. Joke Time l What did pi say to i? l Get real! l What did i say to pi? l Be rational! l What did one-half say to one? l You’re so full of yourself!...
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